NO Initial ITS Start location: __init 0: f1_0_main_ConstantStackPush -> f33_0_loop_GE : arg1'=arg1P0, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2 > 0 /\ -arg1P0-arg2 == 0), cost: 1 1: f33_0_loop_GE -> f33_0_loop_GE : arg1'=arg1P1, arg2'=arg2P1, (-5-arg1P1 == 0 /\ -5-arg1 == 0), cost: 1 2: f33_0_loop_GE -> f33_0_loop_GE : arg1'=arg1P2, arg2'=arg2P2, (arg1 < 0 /\ 5+arg1 < 0 /\ -1+arg1 < 0 /\ 1+arg1-arg1P2 == 0), cost: 1 3: f33_0_loop_GE -> f33_0_loop_GE : arg1'=arg1P3, arg2'=arg2P3, (arg1 < 0 /\ 5+arg1 > 0 /\ -1+arg1 < 0 /\ 1+arg1-arg1P3 == 0), cost: 1 4: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P4, arg2'=arg2P4, TRUE, cost: 1 Applied preprocessing Original rule: f1_0_main_ConstantStackPush -> f33_0_loop_GE : arg1'=arg1P0, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2 > 0 /\ -arg1P0-arg2 == 0), cost: 1 New rule: f1_0_main_ConstantStackPush -> f33_0_loop_GE : arg1'=-arg2, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 Applied preprocessing Original rule: f33_0_loop_GE -> f33_0_loop_GE : arg1'=arg1P1, arg2'=arg2P1, (-5-arg1P1 == 0 /\ -5-arg1 == 0), cost: 1 New rule: f33_0_loop_GE -> f33_0_loop_GE : arg1'=-5, arg2'=arg2P1, 5+arg1 == 0, cost: 1 Applied preprocessing Original rule: f33_0_loop_GE -> f33_0_loop_GE : arg1'=arg1P2, arg2'=arg2P2, (arg1 < 0 /\ 5+arg1 < 0 /\ -1+arg1 < 0 /\ 1+arg1-arg1P2 == 0), cost: 1 New rule: f33_0_loop_GE -> f33_0_loop_GE : arg1'=1+arg1, arg2'=arg2P2, -5-arg1 > 0, cost: 1 Applied preprocessing Original rule: f33_0_loop_GE -> f33_0_loop_GE : arg1'=arg1P3, arg2'=arg2P3, (arg1 < 0 /\ 5+arg1 > 0 /\ -1+arg1 < 0 /\ 1+arg1-arg1P3 == 0), cost: 1 New rule: f33_0_loop_GE -> f33_0_loop_GE : arg1'=1+arg1, arg2'=arg2P3, (5+arg1 > 0 /\ -arg1 > 0), cost: 1 Simplified rules Start location: __init 5: f1_0_main_ConstantStackPush -> f33_0_loop_GE : arg1'=-arg2, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 6: f33_0_loop_GE -> f33_0_loop_GE : arg1'=-5, arg2'=arg2P1, 5+arg1 == 0, cost: 1 7: f33_0_loop_GE -> f33_0_loop_GE : arg1'=1+arg1, arg2'=arg2P2, -5-arg1 > 0, cost: 1 8: f33_0_loop_GE -> f33_0_loop_GE : arg1'=1+arg1, arg2'=arg2P3, (5+arg1 > 0 /\ -arg1 > 0), cost: 1 4: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P4, arg2'=arg2P4, TRUE, cost: 1 Applied nonterm Original rule: f33_0_loop_GE -> f33_0_loop_GE : arg1'=-5, arg2'=arg2P1, 5+arg1 == 0, cost: 1 New rule: f33_0_loop_GE -> [3] : (-5-arg1 >= 0 /\ 5+arg1 >= 0), cost: NONTERM Applied acceleration Original rule: f33_0_loop_GE -> f33_0_loop_GE : arg1'=-5, arg2'=arg2P1, 5+arg1 == 0, cost: 1 New rule: f33_0_loop_GE -> f33_0_loop_GE : arg1'=-5, arg2'=arg2P1, (-5-arg1 >= 0 /\ 5+arg1 >= 0), cost: n2 Applied acceleration Original rule: f33_0_loop_GE -> f33_0_loop_GE : arg1'=1+arg1, arg2'=arg2P2, -5-arg1 > 0, cost: 1 New rule: f33_0_loop_GE -> f33_0_loop_GE : arg1'=arg1+n4, arg2'=arg2P2, (-4-arg1-n4 > 0 /\ -1+n4 >= 0), cost: n4 Applied instantiation Original rule: f33_0_loop_GE -> f33_0_loop_GE : arg1'=arg1+n4, arg2'=arg2P2, (-4-arg1-n4 > 0 /\ -1+n4 >= 0), cost: n4 New rule: f33_0_loop_GE -> f33_0_loop_GE : arg1'=-5, arg2'=arg2P2, (-6-arg1 >= 0 /\ 1 > 0), cost: -5-arg1 Applied acceleration Original rule: f33_0_loop_GE -> f33_0_loop_GE : arg1'=1+arg1, arg2'=arg2P3, (5+arg1 > 0 /\ -arg1 > 0), cost: 1 New rule: f33_0_loop_GE -> f33_0_loop_GE : arg1'=arg1+n6, arg2'=arg2P3, (-1+n6 >= 0 /\ 1-arg1-n6 > 0 /\ 5+arg1 > 0), cost: n6 Applied instantiation Original rule: f33_0_loop_GE -> f33_0_loop_GE : arg1'=arg1+n6, arg2'=arg2P3, (-1+n6 >= 0 /\ 1-arg1-n6 > 0 /\ 5+arg1 > 0), cost: n6 New rule: f33_0_loop_GE -> f33_0_loop_GE : arg1'=0, arg2'=arg2P3, (1 > 0 /\ 5+arg1 > 0 /\ -1-arg1 >= 0), cost: -arg1 Applied simplification Original rule: f33_0_loop_GE -> [3] : (-5-arg1 >= 0 /\ 5+arg1 >= 0), cost: NONTERM New rule: f33_0_loop_GE -> [3] : (5+arg1 <= 0 /\ 5+arg1 >= 0), cost: NONTERM Applied simplification Original rule: f33_0_loop_GE -> f33_0_loop_GE : arg1'=-5, arg2'=arg2P1, (-5-arg1 >= 0 /\ 5+arg1 >= 0), cost: n2 New rule: f33_0_loop_GE -> f33_0_loop_GE : arg1'=-5, arg2'=arg2P1, (5+arg1 <= 0 /\ 5+arg1 >= 0), cost: n2 Applied simplification Original rule: f33_0_loop_GE -> f33_0_loop_GE : arg1'=-5, arg2'=arg2P2, (-6-arg1 >= 0 /\ 1 > 0), cost: -5-arg1 New rule: f33_0_loop_GE -> f33_0_loop_GE : arg1'=-5, arg2'=arg2P2, 6+arg1 <= 0, cost: -5-arg1 Applied simplification Original rule: f33_0_loop_GE -> f33_0_loop_GE : arg1'=0, arg2'=arg2P3, (1 > 0 /\ 5+arg1 > 0 /\ -1-arg1 >= 0), cost: -arg1 New rule: f33_0_loop_GE -> f33_0_loop_GE : arg1'=0, arg2'=arg2P3, (5+arg1 > 0 /\ 1+arg1 <= 0), cost: -arg1 Applied deletion Removed the following rules: 6 7 8 Accelerated simple loops Start location: __init 5: f1_0_main_ConstantStackPush -> f33_0_loop_GE : arg1'=-arg2, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 13: f33_0_loop_GE -> [3] : (5+arg1 <= 0 /\ 5+arg1 >= 0), cost: NONTERM 14: f33_0_loop_GE -> f33_0_loop_GE : arg1'=-5, arg2'=arg2P1, (5+arg1 <= 0 /\ 5+arg1 >= 0), cost: n2 15: f33_0_loop_GE -> f33_0_loop_GE : arg1'=-5, arg2'=arg2P2, 6+arg1 <= 0, cost: -5-arg1 16: f33_0_loop_GE -> f33_0_loop_GE : arg1'=0, arg2'=arg2P3, (5+arg1 > 0 /\ 1+arg1 <= 0), cost: -arg1 4: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P4, arg2'=arg2P4, TRUE, cost: 1 Applied chaining First rule: f1_0_main_ConstantStackPush -> f33_0_loop_GE : arg1'=-arg2, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 Second rule: f33_0_loop_GE -> [3] : (5+arg1 <= 0 /\ 5+arg1 >= 0), cost: NONTERM New rule: f1_0_main_ConstantStackPush -> [3] : (arg1 > 0 /\ -5+arg2 == 0), cost: NONTERM Applied chaining First rule: f1_0_main_ConstantStackPush -> f33_0_loop_GE : arg1'=-arg2, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 Second rule: f33_0_loop_GE -> f33_0_loop_GE : arg1'=-5, arg2'=arg2P1, (5+arg1 <= 0 /\ 5+arg1 >= 0), cost: n2 New rule: f1_0_main_ConstantStackPush -> f33_0_loop_GE : arg1'=-5, arg2'=arg2P1, (arg1 > 0 /\ -5+arg2 == 0), cost: 1+n2 Applied chaining First rule: f1_0_main_ConstantStackPush -> f33_0_loop_GE : arg1'=-arg2, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 Second rule: f33_0_loop_GE -> f33_0_loop_GE : arg1'=-5, arg2'=arg2P2, 6+arg1 <= 0, cost: -5-arg1 New rule: f1_0_main_ConstantStackPush -> f33_0_loop_GE : arg1'=-5, arg2'=arg2P2, (arg1 > 0 /\ -6+arg2 >= 0), cost: -4+arg2 Applied chaining First rule: f1_0_main_ConstantStackPush -> f33_0_loop_GE : arg1'=-arg2, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 Second rule: f33_0_loop_GE -> f33_0_loop_GE : arg1'=0, arg2'=arg2P3, (5+arg1 > 0 /\ 1+arg1 <= 0), cost: -arg1 New rule: f1_0_main_ConstantStackPush -> f33_0_loop_GE : arg1'=0, arg2'=arg2P3, (arg1 > 0 /\ -1+arg2 >= 0 /\ 5-arg2 > 0), cost: 1+arg2 Applied deletion Removed the following rules: 13 14 15 16 Chained accelerated rules with incoming rules Start location: __init 5: f1_0_main_ConstantStackPush -> f33_0_loop_GE : arg1'=-arg2, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 17: f1_0_main_ConstantStackPush -> [3] : (arg1 > 0 /\ -5+arg2 == 0), cost: NONTERM 18: f1_0_main_ConstantStackPush -> f33_0_loop_GE : arg1'=-5, arg2'=arg2P1, (arg1 > 0 /\ -5+arg2 == 0), cost: 1+n2 19: f1_0_main_ConstantStackPush -> f33_0_loop_GE : arg1'=-5, arg2'=arg2P2, (arg1 > 0 /\ -6+arg2 >= 0), cost: -4+arg2 20: f1_0_main_ConstantStackPush -> f33_0_loop_GE : arg1'=0, arg2'=arg2P3, (arg1 > 0 /\ -1+arg2 >= 0 /\ 5-arg2 > 0), cost: 1+arg2 4: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P4, arg2'=arg2P4, TRUE, cost: 1 Removed unreachable locations and irrelevant leafs Start location: __init 17: f1_0_main_ConstantStackPush -> [3] : (arg1 > 0 /\ -5+arg2 == 0), cost: NONTERM 4: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P4, arg2'=arg2P4, TRUE, cost: 1 Eliminating location f1_0_main_ConstantStackPush by chaining: Applied chaining First rule: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P4, arg2'=arg2P4, TRUE, cost: 1 Second rule: f1_0_main_ConstantStackPush -> [3] : (arg1 > 0 /\ -5+arg2 == 0), cost: NONTERM New rule: __init -> [3] : (-5+arg2P4 == 0 /\ arg1P4 > 0), cost: NONTERM Applied deletion Removed the following rules: 4 17 Eliminated locations on linear paths Start location: __init 21: __init -> [3] : (-5+arg2P4 == 0 /\ arg1P4 > 0), cost: NONTERM Computing asymptotic complexity Proved nontermination of rule 21 via SMT. Proved the following lower bound Complexity: Nonterm Cpx degree: Nonterm Solved cost: NONTERM Rule cost: NONTERM Rule guard: (-5+arg2P4 == 0 /\ arg1P4 > 0)